Question

ten years ago a was thrice as old as b was but 12 years hence,a will be only twice as old as b. then the a's present age​

Answer 1

Answer:

Presently A is 76 years old and B is 32 years old

Step-by-step explanation:

Scenario 10 years ago = A was thrice as old as B

Scenario 12 years hence = A will be twice as old as B

Consider the ages 10 years ago as :

• B = x
• A = 3x

Present ages :

• B = (x + 10)
• A = (3x + 10)

Ages 12 years hence :

• B = (x + 10) + 12
• A = (3x + 10) + 12

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According to the question :

12 years hence, A will be only twice as old as B.

⇒ (3x + 10) + 12 = 2[(x + 10) + 12]

⇒ 3x + 22 = 2[x + 22]

⇒ 3x + 22 = 2x + 44

⇒ 3x - 2x = 44 - 22

⇒ x = 22

B is 22 years old (10 years ago)

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Present ages :

A's age =

⇒ 3(22) + 10

⇒ 66 + 10

⇒ 76 years

B's age =

⇒ 22 + 10

⇒ 32 years  

Therefore, presently A is 76 years old and B is 32 years old.

Answer 2

Given :-

Ten years ago a was thrice as old as b was but 12 years hence, a will be only twice as old as b

To Find :-

Age of a

Solution :-

Let us assume that

The present age of b be y

Age of a = 3y

Now

Present age of a = 3y + 10

Present age of b= y + 10

After 12 years

Age of a = (3y + 10) + 12 = 3y + 22

Age of b = (y + 10) + 12 = y +  22

Now

$\sf 3y +22 = 2(y+22)$

$\sf 3y +22 = 2y + 44$

$\sf 3y-2y=44-22$

$\sf y = 22$

Age of a = 3y + 10 = 66 + 10 = 76 years